http://arxiv.org/abs/2006.11935
The geometrical formulation of the quantum Hamilton-Jacobi theory shows that the quantum potential is never vanishing, so that it plays the role of intrinsic energy. Such a key property selects the Wheeler-DeWitt (WDW) quantum potential $Q[g_{jk}]$ as the natural candidate for the dark energy. This leads to the WDW Hamilton-Jacobi equation with a vanishing kinetic term, and with the identification $$ \Lambda=-\frac{\kappa^2}{\sqrt{\bar g}}Q[g_{jk}] \ . $$ This shows that the cosmological constant is a quantum correction of the Einstein tensor, reminiscent of the von Weizs\”acker correction to the kinetic term of the Thomas-Fermi theory. The quantum potential also defines the Madelung pressure tensor. Such a geometrical origin of the vacuum energy density, a strictly non-perturbative phenomenon, provides strong evidence that it is due to a graviton condensate. Time independence of the WDW wave-functional then would imply that the ratio between the Planck length and the Hubble radius is a time constant, providing an infrared/ultraviolet duality. This indicates that the structure of the Universe is crucial for a formulation of Quantum Gravity.
A. Alon, E. Faraggi and M. Matone
Tue, 23 Jun 20
84/84
Comments: 13 pages
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